Solve 21/4div51/2

$$2 \frac { 1 } { 4 } \div 5 \frac { 1 } { 2 }$$

Evaluate

$$\frac{9}{22}\approx 0.409090909$$

Solution Steps

Divide \frac{2\times 4+1}{4} by \frac{5\times 2+1}{2} by multiplying \frac{2\times 4+1}{4} by the reciprocal of \frac{5\times 2+1}{2}.

$$\frac{\left(2\times 4+1\right)\times 2}{4\left(5\times 2+1\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1+2\times 4}{2\left(1+2\times 5\right)}$$

Multiply 2 and 4 to get 8.

$$\frac{1+8}{2\left(1+2\times 5\right)}$$

Add 1 and 8 to get 9.

$$\frac{9}{2\left(1+2\times 5\right)}$$

Multiply 2 and 5 to get 10.

$$\frac{9}{2\left(1+10\right)}$$

Add 1 and 10 to get 11.

$$\frac{9}{2\times 11}$$

Multiply 2 and 11 to get 22.

$$\frac{9}{22}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 11} = 0.4090909090909091$$